How to Calculate and Solve the Centre of Gravity of a Right Circular Cone

This image above is a display of what a right circular cone looks like. There is only one essential parameter for calculating the centroid or centre of gravity of a right circular cone. This parameter is the height of the cone (h).

The formula for calculating the the centroid or centre of gravity of a right circular cone is:

C.G. = h / 4

As always let’s solve an example.

Find the centroid or centre of gravity of a right circular cone where the height of the cone is 12cm.
This implies that:

h = height of the cone = 12

C.G. = 12 / 4
C.G. = 3

Therefore, the centroid or centre of gravity of the right circular cone is 3.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a right circular cone at a distance from its base measured along the vertical axis.

To get the answer and workings to center of gravity or centroid of a right circular cone using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Continue reading How to Calculate and Solve the Centre of Gravity of a Right Circular Cone

How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

It is very possible to compute the centroid or centre of gravity of a circular sector. There are two highly important parameters one needs to know to compute the centre of gravity of a circular sector. These parameters are:

  • Radius of the Sector (r)
  • Semi Vertical Angle (α)

The formula for computing the centre of gravity of a circular sector is:

C.G. = 2rsinα /

Now, let’s take an example.
Let’s find the centroid or the centre of gravity of a circular sector that has a radius of 4m and a semi vertical angle of 30°.
This implies that:

r = Radius of the Sector = 4
α = Semi Vertical Angle = 30

Entering this values into the formula we have:

C.G. = 2(4)sin30° / 3(30)
C.G. = 8 . sin30° / 90
C.G. = 8 . (0.5) / 90
C.G. = 4 / 90
C.G. = 0.0444

Therefore, the centroid or centre of gravity of the circular sector is 0.0444.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a circular sector making a semi vertical angle α at a distance from the centre of the sector measured along the central axis.

To get the answer and workings to center of gravity or centroid of a circular sector. First, you need to obtain the Nickzom Calculator – The Calculator Encyclopedia app.

Continue reading How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

Nickzom Calculator Calculates the Center of Gravity of a Trapezium in Statics Mechanics

According to Quora,

The center of gravity of a trapezoid can be estimated by dividing the trapezoid in two triangles.

Nickzom Calculator calculates the centre of gravity of a trapezium with parallel sides a and b at a distance measured from side b.

The formula for calculating this center of gravity is:

C.G. = h (b + 2a) / 3 (b + a)

Where, a and b are the length of the parallel sides of the trapezium (b being the base length and a being the top length) whereas h is the height of the trapezium.

Let’s take for Example: Find the center of gravity or centroid of a trapezium where a is 4, b is 8 and h is 2.

This implies:

a = 4
b = 8
h = 2

C.G. = 2 (8 + 2(4)) / 3 (8 + 4)
C.G. = 2 (8 + 8) / 3 (12)
C.G. = 2 (16) / 36
C.G. = 32 / 36
C.G. = 0.89

Therefore, the center of gravity or centroid of the trapezium is 0.89.

To get the answer and workings to center of gravity or centroid of a trapezium. First, you need to obtain the Nickzom Calculator – The Calculator Encyclopedia app.

Continue reading Nickzom Calculator Calculates the Center of Gravity of a Trapezium in Statics Mechanics

The Calculator Encyclopedia Calculates the Hydraulic Mean Depth or Hydraulic Radius of Flow in Open Channels | Fluid Mechanics

Hydraulic mean depth or hydraulic radius can be defined as the cross-sectional area of flow divided by wetted perimeter.

Wetted perimeter is the perimeter of the cross sectional area that is “wet”.
Hydraulic mean depth or hydraulic radius is a very important parameter in flow in open channels and fluid mechanics calculations.

The formula for computing hydraulic mean depth or hydraulic radius is:

R = A / P

Where:
R = Hydraulic Depth
A = Cross-sectional Area of Flow
P =  Wetted Perimeter

For Example:

Find the hydraulic mean depth or hydraulic radius of flow in an open channel where the cross-sectional area is 150 m2 and the wetted perimeter is 100 m.

From the example we can see that the cross-sectional area is 150 m2 and the wetted perimeter is 100 m.

R = 150 / 100
R = 1.5

Therefore, the hydraulic mean depth or hydraulic radius is 1.5 m.

Now, I would love to show you how to use Nickzom Calculator The Calculator Encyclopedia to get answers for your questions on hydraulic mean depth or hydraulic radius.

Continue reading The Calculator Encyclopedia Calculates the Hydraulic Mean Depth or Hydraulic Radius of Flow in Open Channels | Fluid Mechanics

Nickzom Calculator Calculates the Hydraulic Depth of Flow in Open Channels | Fluid Mechanics

Hydraulic depth can be defined as the cross-sectional area of flow divided by the top width of surface.

Hydraulic depth is a very crucial parameter in calculations dealing with fluid mechanics and flow in open channels.

The formula for computing hydraulic depth is:

R = A / T

Where:
R = Hydraulic Depth
A = Cross-sectional Area of Flow
T =  Top Width or Top Surface Water Width

For Example:

Find the hydraulic depth of flow in an open channel where the cross-sectional area is 120 m2 and the top width is 12 m.

From the example we can see that the cross-sectional area is 120 m2 and the top width is 12 m.

R = 120 / 12
R = 10

Therefore, the hydraulic depth is 10 m.

Now, I would love to show you how to use Nickzom Calculator The Calculator Encyclopedia to get answers for your questions on hydraulic depth.

Continue reading Nickzom Calculator Calculates the Hydraulic Depth of Flow in Open Channels | Fluid Mechanics

How To Get Answers and Steps For a Function of a Function Differentiation (Calculus) Problem Using The Calculator Encyclopedia

According to Wikipedia,

In mathematicsdifferential calculus is a sub-field of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus, the study of the area beneath a curve.

Nickzom Calculator calculates function of a function for the following formats:

    • (expression)n
    • k(expression)n
    • sin(expression)
    • ksin(expression)
    • cos(expression)
    • kcos(expression)
    • tan(expression)
    • ktan(expression)
    • sinh(expression)
    • ksinh(expression)
    • cosh(expression)
    • kcosh(expression)
    • cot(expression)
    • kcot(expression)
    • cosec(expression)
    • kcosec(expression)
    • In(expression)
    • kIn(expression)
    • loga(expression)
    • kloga(expression)
    • e(expression)
    • ke(expression)
    • a(expression)
    • ka(expression)

k, a and in the formats above represents constants.

The expression represents a polynomial, quadratic or linear mathematical statement, such as:

  • 3x + 5
  • 4x2 + 2x + 1
  • 2x3 + 7x + 12
  • 5x4 + 3x3 + 4x2 + 12x + 15

So implementing the expressions and applying constant numbers here is a list of what the function of a function formats look like that can be solved by Nickzom Calculator and also display the steps (workings).

      • (2x2 + 3x + 5)7
      • 4(2x + 1)6
      • sin(2x2 + 3x + 5)
      • 2sin(3x + 5)
      • cos(3x + 5)
      • 2cos(3x + 5)
      • tan(2x3 + 3x2 + 4x + 5)
      • 3tan(7x + 6)
      • sinh(2x4 + 12)
      • 2sinh(3x + 10)
      • cosh(x5 + 2x3 + 11)
      • 3cosh(2x3 + 12x + 17)
      • cot(2x + 1)
      • 3cot(3x + 5)
      • cosec(x + 12)
      • 7cosec(2x + 7)
      • In(x3 + 2x + 7)
      • 2In(2x2 + 3x + 12)
      • log3(3x + 7)
      • 2log2(x2 + 4x + 8)
      • e(3x + 5)
      • 2e(2x + 3)
      • 2(7x + 2)
      • 7 . 2(6x + 7)

Continue reading How To Get Answers and Steps For a Function of a Function Differentiation (Calculus) Problem Using The Calculator Encyclopedia

Nickzom Calculator Calculates the Total Time of Flight and Time of Flight at Maximum Height in Projectile (Physics)

I am not hear to start explaining to you the meaning and application of time of flight. I believe you are here to know how the calculator encyclopedia calculates these parameters.

Nickzom Calculator requires three parameters to get the answer for time of flight and these parameters are:

  • Acceleration due to Gravity
  • Initial Velocity
  • Angle of Projection

Let’s first get the workings and answer for time of flight at maximum height where the acceleration due to gravity is 10 m/s2, initial velocity is 20 m/s and angle of projection is 30°.

First and Foremost, Select Physics from the home page and click on Open Section

In the Physics section, Click on Projectile

Continue reading Nickzom Calculator Calculates the Total Time of Flight and Time of Flight at Maximum Height in Projectile (Physics)

How to Get Answers of a 2 By 2 Matrix Linear Programming Maximization Problem Without Artificial Variables Using Nickzom Calculator

According to Google Dictionary,

Linear Programming is a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost.

According to Wikipedia,

Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

You might be wondering how possible is it for there to be a calculator that can really solve linear programming calculations and show the workings at the same time. My dear, Nickzom Calculator does that for you at the very best of all capabilities.

Nickzom Calculator can not only solve a 2 by 2 matrix linear programming problem but can also solve for an m by n matrix problem. At the moment, Nickzom Calculator can handle:

  • Maximization Without Artificial Variable(s)
  • Minimization Without Artificial Variable(s)

Computations of Linear Programming with artificial variables is on the way and I do promise to inform you once it is integrated into the calculator encyclopedia via this blog.

Nickzom Calculator makes use of simplex method to compute the result for linear programming problems. There is an iterative computation of steps to obtain the final result which is when there is no further negative entry in the index/third/P row of which a basic solution emerges for x and y variables with all the other variables equal to 0. At this point, the optimal solution and optimal value is given.

Continue reading How to Get Answers of a 2 By 2 Matrix Linear Programming Maximization Problem Without Artificial Variables Using Nickzom Calculator

Nickzom Calculator Calculates the Logarithmic Mean Radius in Heat Transfer of Chemical Engineering

Heat Transfer is one of the major courses every Chemical Engineering student or professional faces at one point in life. There are various sections of heat transfer but for the purpose of this post. Our primary focus is to show you how Nickzom Calculator solves Logarithmic Mean Radius.

To get the answer for Logarithmic Mean Radius in Heat Transfer is very simple and one requires only two parameters which are:

  • Outside Radius of the Cylinder
  • Inside Radius of the Cylinder

Without Further Ado, let me proceed, click on the Calculator Map on Nickzom Calculator+ (Professional Version) – The Calculator Encyclopedia

Clicking on Chemical under Engineering, displays 3 major topics that can be handled by Nickzom Calculator in Chemical Engineering which are:

  • Fluid Mechanics
  • Heat Transfer
  • Mass Transfer

Continue reading Nickzom Calculator Calculates the Logarithmic Mean Radius in Heat Transfer of Chemical Engineering

The Calculator Encyclopedia Calculates the Position of Turning Point for a Vehicle (Vehicle Dynamics)

Calculating the position of turning point for a vehicle must put into consideration the x co-ordinate and y co-ordinate positions of turning point.

There are various parameters you need to be able to calculate these positions. I would start to with how Nickzom Calculator calculates the position of turning point (x co-ordinate).

You are required to have 4 parameters to get the answer for the position and these parameters are:

  • Steer Angle of the Rear Outer Wheel
  • Rear Track
  • Distance of Rear Wheel from Mass Center
  • Steer Angle of Rear Inner Wheel

To access this functionalities in Nickzom Calculator, you need to purchase our professional version – Nickzom Calculator+ (The Calculator Encyclopedia). You can access this software via any of these channels:

Web – https://www.nickzom.org/calculator-plus

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

With that done, Open up the app, select Engineering and click on Open Section.

Click on Mechanical

Then, click on Vehicle Dynamics

Continue reading The Calculator Encyclopedia Calculates the Position of Turning Point for a Vehicle (Vehicle Dynamics)